TY - JOUR
T1 - Multivariate normally distributed biomarkers subject to limits of detection and receiver operating characteristic curve inference
AU - Perkins, Neil J.
AU - Schisterman, Enrique F.
AU - Vexler, Albert
PY - 2013/7
Y1 - 2013/7
N2 - Rationale and Objectives: Biomarkers are of ever-increasing importance to clinical practice and epidemiologic research. Multiple biomarkers are often measured per patient. Measurement of true biomarker levels is limited by laboratory precision, specifically measuring relatively low, or high, biomarker levels resulting in undetectable levels below, or above, a limit of detection (LOD). Ignoring these missing observations or replacing them with a constant are methods commonly used although they have been shown to lead to biased estimates of several parameters of interest, including the area under the receiver operating characteristic (ROC) curve and regression coefficients. Materials and Methods: We developed asymptotically consistent, efficient estimators, via maximum likelihood techniques, for the mean vector and covariance matrix of multivariate normally distributed biomarkers affected by LOD. We also developed an approximation for the Fisher information and covariance matrix for our maximum likelihood estimations (MLEs). We apply these results to an ROC curve setting, generating an MLE for the area under the curve for the best linear combination of multiple biomarkers and accompanying confidence interval. Results: Point and confidence interval estimates are scrutinized by simulation study, with bias and root mean square error and coverage probability, respectively, displaying behavior consistent with MLEs. An example using three polychlorinated biphenyls to classify women with and without endometriosis illustrates how the underlying distribution of multiple biomarkers with LOD can be assessed and display increased discriminatory ability over naïve methods. Conclusions: Properly addressing LODs can lead to optimal biomarker combinations with increased discriminatory ability that may have been ignored because of measurement obstacles.
AB - Rationale and Objectives: Biomarkers are of ever-increasing importance to clinical practice and epidemiologic research. Multiple biomarkers are often measured per patient. Measurement of true biomarker levels is limited by laboratory precision, specifically measuring relatively low, or high, biomarker levels resulting in undetectable levels below, or above, a limit of detection (LOD). Ignoring these missing observations or replacing them with a constant are methods commonly used although they have been shown to lead to biased estimates of several parameters of interest, including the area under the receiver operating characteristic (ROC) curve and regression coefficients. Materials and Methods: We developed asymptotically consistent, efficient estimators, via maximum likelihood techniques, for the mean vector and covariance matrix of multivariate normally distributed biomarkers affected by LOD. We also developed an approximation for the Fisher information and covariance matrix for our maximum likelihood estimations (MLEs). We apply these results to an ROC curve setting, generating an MLE for the area under the curve for the best linear combination of multiple biomarkers and accompanying confidence interval. Results: Point and confidence interval estimates are scrutinized by simulation study, with bias and root mean square error and coverage probability, respectively, displaying behavior consistent with MLEs. An example using three polychlorinated biphenyls to classify women with and without endometriosis illustrates how the underlying distribution of multiple biomarkers with LOD can be assessed and display increased discriminatory ability over naïve methods. Conclusions: Properly addressing LODs can lead to optimal biomarker combinations with increased discriminatory ability that may have been ignored because of measurement obstacles.
KW - Area under the curve
KW - Left censoring
KW - Limit of detection
KW - Maximum likelihood
KW - ROC
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U2 - 10.1016/j.acra.2013.04.001
DO - 10.1016/j.acra.2013.04.001
M3 - Article
C2 - 23747152
AN - SCOPUS:84878947378
VL - 20
SP - 838
EP - 846
JO - Academic Radiology
JF - Academic Radiology
SN - 1076-6332
IS - 7
ER -